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2012 On the augmentation quotients of the IA-automorphism group of a free group
Takao Satoh
Algebr. Geom. Topol. 12(2): 1239-1263 (2012). DOI: 10.2140/agt.2012.12.1239

Abstract

We study the augmentation quotients of the IA-automorphism group of a free group and a free metabelian group. First, for any group G, we construct a lift of the k–th Johnson homomorphism of the automorphism group of G to the k–th augmentation quotient of the IA-automorphism group of G. Then we study the images of these homomorphisms for the case where G is a free group and a free metabelian group. As a corollary, we detect a –free part in each of the augmentation quotients, which can not be detected by the abelianization of the IA-automorphism group.

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Takao Satoh. "On the augmentation quotients of the IA-automorphism group of a free group." Algebr. Geom. Topol. 12 (2) 1239 - 1263, 2012. https://doi.org/10.2140/agt.2012.12.1239

Information

Received: 4 April 2011; Revised: 22 March 2012; Accepted: 23 March 2012; Published: 2012
First available in Project Euclid: 19 December 2017

zbMATH: 1261.20036
MathSciNet: MR2928912
Digital Object Identifier: 10.2140/agt.2012.12.1239

Subjects:
Primary: 20F28
Secondary: 16S34

Rights: Copyright © 2012 Mathematical Sciences Publishers

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Vol.12 • No. 2 • 2012
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